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Tribology International 40 (2007) 1441–1453

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Friction model of a marine diesel engine piston assembly

George A. Livanos�, Nikolaos P. Kyrtatos

Laboratory of Marine Engineering, National Technical University of Athens, 9 Iroon Polytechniou St., Zografos, Athens, Greece

Received 18 July 2006; received in revised form 23 January 2007; accepted 24 January 2007

Available online 26 March 2007

Abstract

In modern marine diesel engines, power output and in-cylinder firing pressures are constantly increasing, leading to higher friction in

engine components and especially in the piston assembly. A good understanding of the friction contributions of the various engine

components is needed, if mechanical efficiency is to be improved. A friction model for the engine piston assembly has been developed and

is presented in this paper. The model, based on lubrication theory, considers the detailed engine geometry and the complete lubricant

action, and thus can be applied to a wide range of engines. In detail, the analysis takes into account the friction components of

compression rings, oil control rings, piston skirt and gudgeon pin of the engine piston assembly. The model was applied to a four-stroke

(medium speed) marine diesel engine and the effect of engine speed and load on friction was examined and compared with results from

other semi-empirical models. The engine friction was predicted at constant rotational speed (generator operation) and variable rotational

speed (propulsion operation).

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Piston; Piston rings; Friction; Piston secondary motion; Engines

1. Introduction

Nowadays, the continuously increasing cost of marinefuel in conjunction with the environmental impacts ofthe operation of internal combustion engines makethe improvement of the engine’s mechanical efficiencyimperative.

A good understanding and measurement of the frictioncontributions of the various engine rotating or oscillatingcomponents is needed, if mechanical efficiency is to beimproved. Towards this direction and since a significantpart of the total power loss in an internal combustionengine is due to piston assembly friction, the contributionof engine piston assembly friction models is important.Such models can be used in computer codes for thecomplete simulation of internal combustion enginesoperation and can reduce the design and development time.

One of the earliest calculations on piston ring andcylinder liner lubrication were made in 1936 by Castleman[1]. Almost 20 years later, Eilion and Saunders [2]

ee front matter r 2007 Elsevier Ltd. All rights reserved.

iboint.2007.01.020

ing author. Tel.: +302107721132.

ess: glivan@naval.ntua.gr (G.A. Livanos).

conducted another lubrication analysis of piston ring andreported the oil film thickness and friction forces. In theseearly studies, the squeeze film effect was neglected and asimplified hydrodynamic lubrication theory was applied.The squeeze film effect was first incorporated into theanalysis by Furuhama [3]. These works were based on fullyflooded inlet condition assumption. However for a ringpack operating in an engine, the lubricant supply is notalways adequate for fully flooded lubrication and starva-tion inlet conditions prevail. Starved ring lubrication wasstudied by many researchers [4–7] applying differentboundary conditions and numerical solution schemes.The work of Dowson et al. [8], Ruddy et al. [9,10], Keribaret al. [11] and Tian et al. [12] has resulted in thedevelopment of more integrated simulations, which includeeffects of ring dynamics and blow by.Although there is a vast literature regarding piston rings

lubrication [1–12] and piston skirt motion [13–16], theliterature regarding the complete piston assembly lubrica-tion is rather poor [17]. In [17] the friction and dynamicmotion of the piston assembly was studied neglecting thefriction developed on piston pin and the interaction ofseveral piston components (rings, bearings and skirts).

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Nomenclature

Ring pack

a ring offsetb ring widthB ring geometry parameterFf friction forceFgas gas force applied on a ring back due to the in-

cylinder pressureFring tension ring force applied on the cylinder liner, due

to the ring elasticityF

ringf ring friction

h lubricant film thicknesshmin minimum oil film thicknesshG ring face profilep oil film pressurepgas inlet gas pressure at the inlet of the ringpgas outlet gas pressure at the outlet of the ringPc contact pressure with surface roughnessPringf ring frictional losses

q lubricant flow rateWoil resultant force from the oil film pressureWexternalexternal load applied on the ringm oil viscosity

Piston skirt

a vertical distance from top of piston skirt to thewrist pin

b vertical distance from top of piston skirt to thepiston center of mass

C radial clearance between piston and cylinderCg distance of the piston center of mass from the

wrist pin axisCp distance of the wrist pin from the geometric axis

of the piston (wrist pin offset)et, eb eccentricities of the piston measured at the top

and bottom of the skirtFfring friction force of the complete ring packFskirt load capacity of the hydrodynamic fluid film of

the piston skirtFgas gas force acting at top of the pistonF inertial

piston_x;Finertialpiston_y inertia forces due to piston mass

F inertialpin_x ;F

inertialpin_y Inertia forces due to wrist pin andconnecting rod small end mass

Frod force along the connecting rodh fluid film thicknessIpiston piston rotary inertia about its center of massL piston skirt lengthMskirt moment about wrist pin due to hydrodynamic

forcesM inertial

piston inertia torque of pistonMgp friction torque of the piston pinmpiston piston massmpin wrist pin and connecting rod small end massp hydrodynamic fluid film pressureR piston radiusU piston sliding velocityx lateral piston motionY piston position measured from top dead centery fluid film axial coordinate measured from top

of skirtm lubricant viscosity

Piston pin bearing

J functionalA areaC clearanceS boundaryH film thicknessP film pressureu average film velocityU average surface velocitym viscosityr densityQ fluid film flowQU pseudo flow (shear)Q_h pseudo flow (squeeze)

K fluidity matrixe bearing eccentricityR bearing radiusD bearing diameterL bearing lengthN interpolation functioni, j nodal indicesx, y film coordinatesn unit normal

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–14531442

The objective of the presented work is the study of thelubrication of the complete piston assembly (rings, skirtand gudgeon pin), solving the coupled system of lubrica-tion and motion equations applied on each piston assemblycomponent. The instant friction of ring pack, piston skirtand piston pin is predicted, and the total mechanical powerloss of piston assembly is calculated. The friction modeldeveloped in this work was applied to a case of a four-stroke marine diesel engine, in contrast to automotive

engines, often used for application of other existingmodels.

2. Theoretical model

The piston friction model, presented in this paperconsiders all the contact surfaces in an engine pistonassembly, i.e. a piston ring pack, a piston skirt and a pistonpin bearing. A lumped crank-slider model was used for the

ARTICLE IN PRESSG.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–1453 1443

calculation of engine component speeds, accelerations andacting forces [18,19]. A description of each piston assemblycomponent modeling follows.

2.1. Piston ring pack model

The proposed model considers that the complete ringpack can be reduced to a set of several compression ringsand one twin-rail oil control ring. Each rail of the oilcontrol ring is manipulated as a separate single ring.

Fig. 1 presents the geometry and the configuration of aring pack consisting of two compression rings and onetwin-rail oil control ring. All rings have barrel shape face,which can be adequately described by a second-orderpolynomial as follows (any ring face profile can beincorporated in the model):

hG ¼ Bðx� aÞ2. (1)

For the simulation of the oil film action between thepiston ring and the cylinder liner, the one-dimensionalReynolds equation is used, considering sliding and squeezering motion:

qqx

h3

12mqp

qx

� �¼

1

2uqh

qxþ

qh

qt, (2)

where u is the piston velocity, p is the developed pressure, mis the oil viscosity and h is the oil film thickness betweenring and cylinder liner and is expressed as follows:

h ¼ hmin þ hG, (3)

Fig. 1. Piston ring pack configuration.

where hmin is the minimum oil film thickness and hG thering face profile.Considering quasi-steady-state conditions, the net resul-

tant force of the fluid film pressure Woil should be inequilibrium with the applied load (from in-cylinder gas Fgas

and ring tension Fring tension) Wexternal at all times. This isexpressed as follows:

Woil ¼

Z xoutlet

xinlet

pdA ¼ Fgas þ F ring tension ¼W external. (4)

It can be concluded from the Reynolds equation (2) andthe force equilibrium equation (4) that there are fourunknowns, these being the pressure p, the minimum oil filmthickness hmin, the position of lubricant inlet xinlet and theposition of lubricant outlet xoutlet. In order to solve theseequations, boundary conditions are applied at both ends(inlet and outlet) of each ring of the complete ring pack.There are several approaches to follow regarding the

boundary conditions applied on piston rings. Priest et al.[20] provides an excellent review of such boundaryconditions. In the work presented here, the approach ofJeng [4] was adopted.

2.1.1. Inlet boundary conditions

The model applies fully flooded inlet conditions for thesecond rail of the oil control ring during the downstrokes,since adequate mass of lubricant is available. On the otherhand, starved lubrication conditions are applied to the restof the rings during the downstrokes and to the completering pack during the upstrokes. These boundary equationsare expressed as follows:

Fully flooded condition : pðxinletÞ ¼ pgas inlet,

xinlet ¼b

2, ð5Þ

Starved condition : pðxinletÞ ¼ pgas inlet,

qðxinletÞ ¼ qavailable. ð6Þ

Note that, in the case of fully flooded conditions, the oilfilm inlet is defined explicitly, while in the case of cavitationboundary condition, the oil film inlet is defined implicitly,through the oil flow equilibrium.

2.1.2. Outlet boundary conditions

The convergent–divergent shape of the ring face profilesuggests that the lubricant film may rupture due tocavitation. The cavitation is considered by applying theReynolds boundary conditions, which are expressed asfollows:

pðxoutletÞ ¼ pgas cavitation ¼ 0,

qp

qxðxoutletÞ ¼ 0 ð7Þ

In Reynolds boundary conditions, the cavitation pointxoutlet is defined implicitly. When the piston approaches thetop dead center (TDC) or bottom dead center (BDC), the

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Piston skirt bearing

surface

θ = 0

θ

θ = π

et

Thru

st s

ide

Anti-th

rust s

id

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–14531444

squeeze motion of piston rings is predominant andcavitation is unlikely to occur. In this case, the exitboundary condition is expressed as

pðxoutletÞ ¼ pgas outlet,

xoutlet ¼b

2. ð8Þ

In the case of no cavitation, the position of lubricant outletis known and it coincides with the outlet edge of the ring(explicitly defined).

Thus, the lubrication mechanism of piston ring pack ismodeled as a well-defined problem described by twoequations (2) and (4) and two sets of boundary conditions(5) or (6) and (7) or (8).

When the piston approaches the TDC or BDC, thereduced ring speed in conjunction with the increasedapplied load may lead to dry contact of the piston ringwith the cylinder liner. To calculate the contact pressure Pc

with surface roughness, the asperity contact model ofGreenwood and Tripp [21] was used. For simplicity innumerical calculations, this model has been defined as anon-linear curve fitting formula by Hu et al. [22].

eb

e

Fig. 2. Piston skirt eccentricities terminology.

2.1.3. Calculation of friction losses

After determining the asperity contact load and thehydrodynamic pressure field of the lubricant, the frictionforce is calculated as follows:

Fringf ¼

ZZtdAþ cf

ZZPc dAc, (9)

where t ¼ ðh=2Þðqp=qxÞ � mðu=hÞ is the fluid shear stress.When hydrodynamic lubrication prevails, the equa-

tion derived by Booker [23] is used to calculate the powerloss:

Pringf ¼

ZZmh

u2 dAþ

ZZh3

12mðrpÞ2 dA. (10)

This equation is preferred because it includes the powerloss due to squeeze piston ring motion.

2.2. Piston skirt model

The friction model presented in this paper incorporates ahydrodynamic lubrication model of the piston skirt, andallows the piston motion and the associated skirt friction tobe calculated as function of engine crank angle (CA).

It is well known from existing literature [13–17] that thepiston executes small translations and rotations within theconfinement of the cylinder clearance (piston secondarymotion). These motions can be defined by the pistoneccentricities ‘‘et’’ and ‘‘eb’’ at the top and bottom of theskirt, respectively (Fig. 2).

The governing equation for the dynamic motion of thepiston can be obtained as follows.

Equilibrium of forces and moments about the pistonwrist-pin requires that (Fig. 3)X

F x ¼ 03F skirt þ F inertialpin_x þ F inertial

piston_x � F rod sin j ¼ 0,

(11)

XFy ¼ 03F gas þ F fring þ F fskirt þ F inertial

pin_y þ F inertialpiston_y

þ F rod cos j ¼ 0, ð12Þ

XM ¼ 03Mskirt þM inertial

piston þ F inertialpiston_xða� bÞ

� F inertialpiston_yCg þ FgasCp þ F fringCp þMfskirt þMgp ¼ 0.ð13Þ

Eliminating Frod from Eqs. (11) and (12) and consideringthat piston inertial forces are calculated from the followingequations:

F inertialpin_y ¼ �mpin

€Y , (14)

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Fgas

Cg Cp

FrodFfskirt

Ffring

inertialFpiston_y Mskirt + Mfskirt

L

αFpiston_xinertial

Fpin_yinertial

Fskirt + Fpin_xinertial

β

x (+)

y (+)

Fig. 3. Forces and moments acting on piston.

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–1453 1445

F inertialpiston_y ¼ �mpiston

€Y , (15)

F inertialpin_x ¼ �mpin €et þ

aLð€eb � €etÞ

h i, (16)

F inertialpiston_x ¼ �mpiston €et þ

bLð€eb � €etÞ

� �, (17)

M inertialpiston ¼ �Ipistonð€et � €ebÞ=L, (18)

the governing equation of piston motion yields

mpiston 1� bL

� �þmpin 1� a

L

� mpiston

bL

� �þmpin

aL

� Ipiston

Lþmpistonða� bÞ 1� b

L

� ��

IpistonLþmpistonða� bÞ b

L

� �2664

3775 €et

€eb

" #

¼

F skirt þ ðF fskirt þ F fring þ Fgas þ F inertialpistony þ F inertial

piny Þ tan f

Mskirt þM fskirt þ F fringCp þMgp þ FgasCP � F inertialpistonyCg

24

35.ð19Þ

The forces and moments, Fskirt, Ffskirt, M and Mfskirt, aredue to the hydrodynamic pressure developed in the oil filmin the load bearing arcs. In contrast to the literature[13–17], the presented model couples the motion of pistonskirt with the motion of piston rings and piston gudgeonpin via the introduction of force Ffring, which is the totalring pack friction, and via the introduction of momentsFringCp and Mgp, which are the moment of completering pack friction about the piston wrist pin and thefriction moment of the piston gudgeon pin bearing,respectively.

The hydrodynamic pressure generation around thepiston skirt is governed by the Reynolds equation as

follows:

qqy

h3 qp

qy

� �þ R2 q

qyh3 qp

qy

� �¼ �6mUR2 qh

qyþ 12mR2 qh

qt.

(20)

Since eb and et are well below L, the oil film thickness canbe approximated by

h ¼ C þ et cos yþy

LCðeb � etÞ cos y. (21)

A Finite Element Scheme is adopted for the solution of thisequation. The following boundary conditions are applied:

qp

qyðy ¼ 0Þ ¼

qp

qyðy ¼ pÞ ¼ 0, (22)

due to symmetry along center line plane. p ¼ pamb, at theedge of the skirt, where pamb is some ambient pressurecondition in the piston skirt region.The equations of motion together with the two-dimen-

sional Reynolds equation describe the motion and lubrica-tion of the piston skirt. After the solution of this set ofcoupled equations, the skirt motion and the lubricantpressure field can be determined, and thus the frictionallosses can be calculated after the integration of thedeveloped shear stresses over the piston skirt lubricatedarea. The procedure is the same as that described in thecase of piston rings model. More information regarding themethod of solution of the system of coupled differentialequations can be found in the literature [13–17].

2.3. Journal bearings model

Friction losses from the piston gudgeon pin bearing arealso included in the proposed friction model. The pistonpin bearing carries loads that vary in magnitude anddirection. The angular velocity of load and sleeve also varyin direction and magnitude.Several approaches have been adopted for the dynamic

investigation of bearings. There are in literature analyticalmodels for short [24], long and finite loaded bearings [25],numerical models that apply the Finite Element Method tosolve the Reynolds equation either in the simple case ofisothermal conditions [26] or in the more complicated case ofelastohydrodynamic lubrication (EHL) [27–29] or thermo-elasto-hydrodynamic lubrication (TEHL) [30,31]. The FiniteElement Scheme with isothermal conditions assumption,presented by Goenka [26], was adopted in this work and willbe outlined here for completeness and to establish notation.

2.3.1. Bearing lubrication model

In the FEM formulation, the pressure distribution in anincompressible lubricant film minimizes the followingfunctional [26,28]:

J ¼1

2

ZA

rh3

12mrp � rpdA�

ZA

rhU � rpdAþ

ZA

rqh

qtpdA

þ

ZSq

rhu � npdS, ð23Þ

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θ

ex

ey

Fig. 4. Journal bearing configuration.

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–14531446

where the film thickness h (Fig. 4) and its rate of change _hare as follows:

h ¼ C � ex cos y� ey sin y,

_h ¼ �_ex cos y� _ey sin y.

Discretization of the pressure field as

pðx; yÞ ¼X

i

Niðx; yÞpi (24)

and substitution in the functional yields

J ¼ �1

2

Xi

Xj

pi Kij pj �X

i

pi QUi þQ

_hi þQ

_ri � qi

� �,

(25)

where

Kij � �

ZA

rh3

12mrNi � rNj dA, (26)

QUi �

ZA

rhU � rNi dA, (27)

Q_hi � �

ZA

rqh

qtNi dA, (28)

qi �

ZSq

rhu � nNi dS. (29)

By setting ðqJ=qpiÞ ¼ 0, we obtain the following linearn� n system:

qi ¼X

j

Kijpj þQUi þQ

_hi . (30)

According to Eq. (30), flow outward from the system isconsidered as a consequence of spatial pressure variation p,surface shear action QU and squeeze action Q

_h. In thiscontext, there are four nodal variables p, q, QU and Q

_h.Considering that bearing motion is known (squeezevelocities), the following cases are obtained:

Case 1: Internal node, full film region (FFR): The nodalvariables QU , Q

_h and q( ¼ 0) are known, whereas node

pressure is the only unknown which is obtained by solvingthe linear system of Eq. (30).

Case 2: Boundary node, (FFR): The nodal variables QU ,Q_h and p( ¼ pboundary) are known, whereas node flow q is

the only unknown which is obtained by solving the linearsystem of Eq. (30).

Case 3: Cavitation region: In the cavitation region isassumed that nodal pressure vanishes (p ¼ 0), and thefollowing relation holds:X

j

Kij pj þQUi þQ

_hi � qio0. (31)

Thus, the problem reduces in defining FFR andcavitation region. The division of the two regions isachieved through an iterative procedure. Initially eachnode is arbitrarily assigned either in FFR or cavitationregion. In the FFR, the node pressure is defined by solvingthe linear system (30), whereas in the rest region (cavitated)the node pressure is zero. After the calculation of pressureprofile in the complete region, it is checked if pressure isalways positive in full fluid region and if Eq. (31) holds incavitation region. For those nodes for which the con-straints are not satisfied, they are transferred to theopposite region (from FFR to cavitation region and viceversa). Several iterations will be required to get the correctboundary for the first time step. However, for thesubsequent time steps the new region assignment will beonly a few nodes off from the previous time step.Once the nodal pressures have been computed, the

resultant forces on the sleeve are obtained as follows:ZA

p cos yRdydZ ¼W x;ZA

p sin yRdydZ ¼W y. ð32Þ

In the solution method [26] adopted in this work,squeeze velocity _h is solved explicitly and simultaneouslywith pressure. In this method, instead of solving n

unknown pressures (n: number of mesh nodes), n+2unknowns (n nodal pressures and 2 components of squeezevelocities) are solved simultaneously. Besides the n-equations (30), two additional equations are obtainedfrom (32).After determining the pressure field developed around

piston pin bearing, the power losses are easily calculatedusing the method presented in the case of piston rings.

3. Model implementation

The presented model was implemented using MATLAB/SIMULINK. The developed SIMULINK simulation plat-form considers the interaction between the ring pack, thepiston pin bearing and the piston skirt module, as shown inFig. 5. Each module implements the relevant theorypresented in the previous section, and defines the pistonrings (h1_dot, h2_dot, h3_dot and h4_dot), the piston pin(ex_dot, ey_dot) and the piston skirt speeds (et_dot,

ARTICLE IN PRESS

h1h2

h3

h4

ex_dot

ey_dot

ex

ey

Ring Pack Friction

Piston Pin Friction

et_dot

eb_dot

et

eb

skirt friction

P_CYL

in_cylinder_pressure

RPM

engine_speed RING PACK MODULE

PISTON SKIRT MODULE

PISTON PIN BEARING MODULE

1s

Integrator7

1s

Integrator6

1s

Integrator5

1s

Integrator4

1s

1s

1s

1s

em

em

em

Fig. 5. Complete piston assembly model layout.

Table 1

MAN B&W L16/24 main particulars

Bore 0.160m

Stroke 0.240m

Power per cylinder 100 kw

Speed 1200 rpm

Compression ratio 15.5:1

Max. combustion pressure 180 bar

Mean effective pressure 20.7 bar

Mean piston speed 9.6m/s

0

2E-006

4E-006

6E-006

8E-006

1E-005

hm

in [m

]

25% LOAD

50% LOAD

75% LOAD

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–1453 1447

eb_dot). After the integration of the predicted speeds, thepiston assembly components motion can be predictedand thus the developed friction forces can be calculated.It is to note that the total ring pack friction and thepiston pin friction predicted by ring pack module andpiston pin bearing module, respectively, enter the pistonskirt module and influence the skirt motion and therelevant skirt friction. Thus more realistic predictions areobtained.

4. Simulation results and discussion

The proposed piston assembly friction model was usedwith geometry data of a single cylinder unit of the MANB&W 5L16/24 four-stroke marine diesel engine, installed inthe test-bed of the Laboratory of Marine Engineering ofthe National Technical University of Athens. The enginemain particulars are listed in Table 1.

The MAN B&W 5L16/24 engine consists of five cylinderunits. The piston of each unit is equipped with twocompression rings and one twin-rail oil control ring. Forthe engine lubrication, a SAE 40 lubricant is used.

The friction of each component of piston assembly wascalculated for several engine operating points at constantspeed (generator operation) and along the propeller curve(propulsion operation). In detail, the following cases wereexamined:

Constant speed cases:

0 200 400 600 800

crank angle [deg]

� 25% nominal load at 1200 rpm,

Fig. 6. Minimum oil film thickness for the first compression ring of piston

� 50% nominal load at 1200 rpm,

assembly for several engine operating points at constant speed.

� 75% nominal load at 1200 rpm.

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Fig

for

Fig

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–14531448

Propeller curve cases:

�

26% nominal load at 756 rpm, � 51% nominal load at 952 rpm, � 86% nominal load at 1137 rpm.

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

xin

[m

]

0 200 400 600 800

crank angle [deg]

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

xc [m

]

25 % LOAD

50% LOAD

75 % LOAD

. 7. Lubricant inlet attachment point xin and cavitation boundary xc

the first compression ring of piston assembly.

0 200 400 600 800

crank angle [deg]

0

4000

8000

12000

16000

20000

fric

tion losses [W

]

25% LOAD

50% LOAD

75% LOAD

ba

. 8. Friction losses of the first compression ring for several engine operati

The contribution of each engine component to the totalengine frictional losses is presented in the next sections.

4.1. Piston rings friction contribution

Fig. 6 presents the minimum oil film thickness variation ofthe first compression ring over a complete engine cycle (720CA degrees) under starved lubrication conditions for threeengine operating points (25%, 50% and 75%) at constantspeed (1200 rpm). It can be seen that the oil film thicknessreduces with increasing the load. As the load increases, thein-cylinder pressure also increases, and the piston ring isfurther forced towards the cylinder liner, leading to decreasein the oil film thickness. The minimum oil film thickness ofthe ring increases with the piston speed, since the higherspeed promotes the hydrodynamic lubrication and theincreased loading capacity of the ring. On the other hand,the oil film thickness is very limited around the TDC andBDC, where boundary lubrication prevails. It must also to bementioned that although the external load applied on thefirst compression ring during the exhaust stroke is lower thanthe ring applied load during the expansion stroke, theminimum oil film thickness in the first case (exhaust stroke) isalso limited due to the low oil availability after the passage ofthe ring pack in the expansion stroke.Fig. 7 depicts the position of oil attachment at the

leading edge of the first compression ring (xin) and theposition where the cavitation begins at the trailing edge ofthe ring (xc), respectively, for several operating points(25%, 50% and 75%) at constant speed (1200 rpm). As canbe observed, the cavitation extends from the trailing ringedge (b/2 during the downward motion of the piston or �b/2 during the upward motion of the piston) to the mid of thering width during the piston stroke. Only around the TDCand BDC, the cavitation is very limited, since the squeezering motion prevails. Note that the peaks in xin and xc

observed in TDC and BDC result from the fact that thetrailing ring edge is converted to leading edge (due topiston speed change) and vice versa.

0 200 400 600 800

crank angle [deg]

0

4000

8000

12000

16000

20000

fric

tion lo

sses [W

]

26% LOAD

51% LOAD

86% LOAD

ng points (a) at constant speed and (b) at variable speed propeller curve.

ARTICLE IN PRESS

-4E-005

-2E-005

0

2E-005

4E-005

6E-005

et, e

b [m

]

25% LOAD

50% LOAD

75% LOAD

et

eb

0 200 400 600 800

crank angle [deg]

-4E-005

-2E-005

0

2E-005

4E-005

6E-005

8E-005

et, e

b [m

]

26% LOAD

51% LOAD

86% LOAD

et

eb

Fig. 9. Piston skirt eccentricity for several engine operating points (a) at

constant speed—generator operation and (b) at variable speed—propul-

sion operation.

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–1453 1449

Figs. 8(a) and (b) present the power loss of the firstcompression ring for constant speed and propeller curveoperation, respectively. The power loss for the part of thestroke where the ring is boundary lubricated (around TDCfiring—3 CA deg.) is significantly higher than the powerloss where the ring is hydrodynamically lubricated. Exceptat the TDC of the firing cycle, the power loss is limitedaround the other dead centers due to the combination ofthe hydrodynamic lubrication and limited speed.

4.2. Piston skirt friction contribution

In the analysis presented here, a perfect cylindricalpiston skirt profile is assumed (no barreling).

Fig. 9(a) presents the piston skirt eccentricities during acomplete engine cycle for several loads at constant speed(1200 rpm). The sign convention for et and eb is that (+)means towards the anti-thrust side and (�) means towardsthe thrust side. During the expansion stroke (from CA0deg. to 180 deg.), the bottom of the piston moves towardsthe anti-thrust side and the top moves towards the thrustside. During the exhaust stroke (from CA 180 deg. to360 deg.), the bottom of the piston moves towards thethrust side and the top oscillates. During the intake stroke(from CA 360 deg. to 540 deg.), both top and bottom of thepiston move towards the anti-thrust side. Finally, duringthe compression, the top of the piston moves towards theanti-thrust side and the bottom of the piston movestowards thrust side. Since the total considered clearancebetween piston and cylinder liner is 63 mm and themaximum piston translation is approximately 53 mmduring expansion stroke at 75% load, the total piston slapis considered very significant during expansion. The pistontrajectory is also presented in Fig. 9(b) for several engineoperating points along the propeller curve. As can be seen,increased piston slap occurs during expansion stroke,whereas average piston oscillation is observed during therest of engine cycle.

Fig. 10 presents the friction force developed on thepiston skirt for constant speed engine operation (a) and forengine operation along a propeller curve (b) at severalloads. In the case of constant speed operation, the pistonskirt friction force is almost independent from the load.This can be explained from the hydrodynamic lubricationconditions prevailing on piston skirt surfaces. In suchconditions, the friction shear stresses are strongly propor-tional to piston speed (and thus to crankshaft rotationalspeed), which is constant in this case. The friction forceexhibits maximum values in the mid-strokes, due to theincreased piston speed, and it reaches minimum values atthe vicinity of dead centers, due to the low piston speed. Onthe other hand in the case of operation along the propellercurve, significant changes in friction force predictions areobserved. The losses increase with the engine speed and thisresults again from the prevailing hydrodynamic conditions.

In Fig. 11, the hydrodynamic force applied on pistonskirt is presented. Increased forces are observed during

expansion stroke (0–360 deg.), due to increased in-cylinderpressure (combustion). This force mainly urges the pistonassembly to move towards anti-thrust side of cylinder linerduring expansion, as was earlier mentioned.

4.3. Piston pin bearing friction contribution

The proposed friction model of piston assembly con-siders that the gudgeon pin bearing belongs to pistonassembly of a single cylinder unit. It is assumed that thisbearing is a plain journal bearing and no geometricaldetails (e.g. grooves, oil holes) are considered.The predicted minimum oil film thickness in the case of

piston pin bearing for variable speed operation and con-stant speed operation is presented in Figs. 12(a) and (b),

ARTICLE IN PRESSG.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–14531450

respectively. It can be seen that the oil film thicknessdecreases with the increasing engine load. This decrease issmaller in the case of engine operation along the propellercurve, due to the fact that the engine speed increases inparallel with the load. Consequently, the increased appliedload is compensated by the increased hydrodynamic loadcapacity (which results from the increased speed) and thisleads to limited reduction of the oil film thickness.

Fig. 13 presents the power losses in the piston pinbearing for (a) constant engine speed operation and (b)engine operation along the propeller curve at several loads.

During constant speed engine operation, the power lossis limited dependent of the load through the cycle, except in

-600

-400

-200

0

200

400

Skirt F

riction [N

]

25% LOAD

50% LOAD

75% LOAD

0 200 400 600 800

crank angle [deg]

-600

-400

-200

0

200

400

Skirt F

riction [N

]

26% LOAD

51% LOAD

86% LOAD

a

b

Fig. 10. Piston skirt friction force for several engine operating points: (a)

at constant speed—generator operation and (b) variable speed—propul-

sion operation.

the vicinity of the TDC firing. It can be seen from thisfigure that piston pin power loss is proportional with itsspeed and inversely proportional with minimum oil filmthickness.In the case of engine operation along the propeller curve

(Fig. 13(b)), the power loss increases significantly with theload, due to the significant speed increase (the power loss isstrongly proportional to the speed).

4.4. Total friction

The total predicted friction losses for a single cylinderunit of the MAN B&W diesel engine are presented in

-10000

0

10000

20000

30000

40000

Hydro

dynam

ic S

kirt F

orc

e [N

]25% LOAD

50% LOAD

75% LOAD

0 200 400 600 800

crank angle [deg]

-10000

0

10000

20000

30000

40000

Hydro

dynam

ic S

kirt F

orc

e [N

]

26% LOAD

51% LOAD

86% LOAD

a

b

Fig. 11. Piston skirt hydrodynamic force for several engine operating

points: (a) at constant speed—generator operation and (b) variable

speed—propulsion operation.

ARTICLE IN PRESS

0

20

40

60

pow

er

losses [W

]

25% LOAD

50% LOAD

75% LOAD

0 200 400 600 800

crank angle [deg]

0

20

40

60pow

er lo

sses [W

]

26% LOAD

51% LOAD

86% LOAD

Fig. 13. Power losses of the piston pin bearing for several engine

operating points (a) at constant speed and (b) at variable speed propeller

curve.

Table 2

Frictional losses for constant speed engine operation

Friction contributions (constant speed operation)

Load 25% 50% 75%

1st compression ring (W) 462.96 720.19 1070.4

2nd compression ring (W) 313.43 386.42 462.22

Oil control ring (W) 259.29 318.2 373.95

Piston skirt (W) 2359.6 2392.2 2428.1

Piston pin (W) 14.5 15.9 17.4

FMEP (bar) 0.7066 0.794 0.901

0

4E-005

8E-005

0.00012

hm

in [m

]

25% LOAD

50% LOAD

75% LOAD

0 200 400 600 800

crank angle [deg]

0

4E-005

8E-005

0.00012

hm

in [m

]

26% LOAD

51% LOAD

86% LOAD

Fig. 12. Minimum oil film thickness of the piston pin bearing for several

engine operating points (a) at variable speed propeller curve and (b) at

constant speed.

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–1453 1451

Tables 2 and 3 for constant speed operation and propellercurve operation, respectively. The piston skirt has thelargest friction contribution and the piston gudgeon pinhas the lowest contribution. It is to be mentioned that thepredicted piston skirt friction contribution in total pistonassembly friction is higher compared with values found inliterature [32] for automotive engines. This can beattributed to the proportional larger piston skirt of amarine diesel engine (skirt length to bore ratio ¼ 1.2)compared to a typical piston skirt of an automotive engine(skirt length to bore ratio ¼ 0.4) [15]. As a result,proportional larger lubricated areas are developed aroundthe piston skirt and increased friction contribution isobserved.

ARTICLE IN PRESS

Table 3

Frictional Losses for variable speed engine operation

Friction contributions (propeller curve operation)

Load 26% 51% 86%

1st compression ring (W) 299.8 580.35 1155.1

2nd compression ring (W) 171.45 285.24 463.54

Oil control ring (W) 142 232 366

Piston skirt (W) 952.74 1518.8 2203.1

Piston pin (W) 5.9 10.3 16.9

FMEP (bar) 0.343 0.686 1.383

Table 4

Fuel power distribution per cylinder for constant speed operation

Load 25% 50% 75%

Piston assembly power loss (kW) 3.41 3.83 4.35

Brake power per cylinder (kW) 25 50 75

Fuel power (kW) 68.2 117.4 167.2

Piston assembly power loss: % of fuel power 5 3.3 2.6

Piston assembly power loss: % of brake power 13.6 7.7 5.8

20 30 40 50 60 70 80

LOAD [%]

0

0.4

0.8

1.2

1.6

F.M

.E.P

. [b

ar]

proposed model

Rezeka

Patton

20 40 60 80 100

0

0.4

0.8

1.2

1.6

F.M

.E.P

. [b

ar]

proposed model

Rezeka

Patton

Fig. 14. Piston assembly power losses in terms of friction mean effective

pressure (FMEP) for several engine operating points (a) at constant speed

and (b) at variable speed (propeller curve operation).

G.A. Livanos, N.P. Kyrtatos / Tribology International 40 (2007) 1441–14531452

The fuel power distribution for several operating pointsat constant speed is presented in Table 4. As can be seen,the total piston assembly power loss accounts for 2.6–5%of fuel power and 5.8–13.6% of brake power. Based onthese data, a 20% reduction in piston assembly losseswould lead to a 0.52–1% reduction in fuel consumption.Even such reductions are considered significant (from shipoperating viewpoint) in the case of large ship propulsionplants of thousands kWs operating at full load, 300 daysper year.

A comparison of the predicted results with resultsobtained from semi-empirical FMEP formulas (Rezekaand Henein [33], Bishop [34], Patton et al. [35]) is presentedin Fig. 14. Although there are differences between theseveral FMEP formulas and the predicted results, theproposed model provides a satisfactory correlation to theseformulas since it predicts overall similar values and trends.

5. Conclusions

A general-purpose engine piston assembly friction modelis proposed in this study. The model is capable ofpredicting the frictional losses of each piston assemblycomponent (piston rings, piston skirts and gudgeon pin)independently.

The model was used with geometrical data from a four-stroke medium-speed marine diesel engine installed in theNTUA Laboratory of Marine Engineering test-bed. Theeffect of engine speed and engine load on predicted pistonassembly friction losses was examined and compared withresults obtained from other semi-empirical FMEP models.It was found that the new model follows the trends of theexisting models, having at the same time the advantage of

detailed simulation of lubrication conditions prevailing onpiston assembly.

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